Project Summary/Abstract HIV remains prevalent among underserved populations in the United States and large parts of sub-Saharan Africa, prompting a strong public health focus on combination HIV prevention practices and pre-exposure pro- phylaxis (PrEP). Cluster-randomized trials (CRTs) are integral to the study of these HIV prevention methods. By collectively randomizing groups of individuals to the same treatment assignment, cluster-randomized designs minimize contamination between trial arms and make feasible the study of community-level prevention efforts. Stepped-wedge cluster-randomized trials (SW-CRTs) are a recent modi?cation of this design involving unidi- rectional crossover from standard-of-care to intervention. However, cluster randomization induces correlation between observations in the same cluster, and these observations are often repeatedly assessed for the out- come of interest. Existing statistical methods for clinical trial design and monitoring fail to address such complex data structures, limiting investigators' ability to conduct statistically rigorous CRTs for HIV prevention. This proposal addresses this methodological gap by (1) developing interim monitoring methods for CRTs with interval-censored endpoints and (2) developing power and sample size methods for SW-CRTs with multiple levels of clustering and longitudinal follow-up. Interval-censoring occurs in HIV prevention trials when the time- to-event outcome of interest is assessed only at intermittent clinic visits. While interim monitoring methods exist for clustered data and for time-to-event data separately, no methods currently handle both clustered and interval- censored observations. One statistical tool commonly used for interim monitoring is the conditional power, the conditional probability of detecting a signi?cant preventative effect at the end of the trial given both the observed interim data and a set of assumptions about the remainder of the study. Aim 1 proposes a simulation-based approach to calculating the conditional power of CRTs with interval-censored endpoints. Aim 2 develops sample size and power formulae for SW-CRTs with hierarchical clustering and longitudinal follow-up. Such dependence structures arise naturally in HIV prevention studies, as, for example, patients are clustered within physicians who are grouped within hospitals, and these patients are then monitored over time for HIV seroconversion. No sample size or power methods for stepped-wedge cluster-randomized trials directly address this data structure. Current stepped-wedge trials may be inappropriately powered as a result, making it dif?cult for investigators to detect pertinent prevention effects. Thus, the methods developed under this proposal will improve the feasibility of conducting the innovative, cluster-randomized HIV prevention studies needed to evaluate the effectiveness of and patient adherence to PrEP in at-risk populations, and to determine the best ways to implement combination HIV prevention strategies.